Deep learning techniques for inverse problems in imaging

G Ongie, A Jalal, CA Metzler… - IEEE Journal on …, 2020 - ieeexplore.ieee.org
Recent work in machine learning shows that deep neural networks can be used to solve a
wide variety of inverse problems arising in computational imaging. We explore the central …

Deterministic equivalent and error universality of deep random features learning

D Schröder, H Cui, D Dmitriev… - … on Machine Learning, 2023 - proceedings.mlr.press
This manuscript considers the problem of learning a random Gaussian network function
using a fully connected network with frozen intermediate layers and trainable readout layer …

Online stochastic gradient descent on non-convex losses from high-dimensional inference

GB Arous, R Gheissari, A Jagannath - Journal of Machine Learning …, 2021 - jmlr.org
Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising
in high-dimensional inference tasks. Here one produces an estimator of an unknown …

Instance-optimal compressed sensing via posterior sampling

A Jalal, S Karmalkar, AG Dimakis, E Price - arXiv preprint arXiv …, 2021 - arxiv.org
We characterize the measurement complexity of compressed sensing of signals drawn from
a known prior distribution, even when the support of the prior is the entire space (rather than …

A non-asymptotic framework for approximate message passing in spiked models

G Li, Y Wei - arXiv preprint arXiv:2208.03313, 2022 - arxiv.org
Approximate message passing (AMP) emerges as an effective iterative paradigm for solving
high-dimensional statistical problems. However, prior AMP theory--which focused mostly on …

Phase retrieval in high dimensions: Statistical and computational phase transitions

A Maillard, B Loureiro, F Krzakala… - Advances in Neural …, 2020 - proceedings.neurips.cc
We consider the phase retrieval problem of reconstructing a $ n $-dimensional real or
complex signal $\mathbf {X}^\star $ from $ m $(possibly noisy) observations $ Y_\mu=|\sum …

Robust compressed sensing using generative models

A Jalal, L Liu, AG Dimakis… - Advances in Neural …, 2020 - proceedings.neurips.cc
We consider estimating a high dimensional signal in $\R^ n $ using a sublinear number of
linear measurements. In analogy to classical compressed sensing, here we assume a …

Towards sample-optimal compressive phase retrieval with sparse and generative priors

Z Liu, S Ghosh, J Scarlett - Advances in Neural Information …, 2021 - proceedings.neurips.cc
Compressive phase retrieval is a popular variant of the standard compressive sensing
problem in which the measurements only contain magnitude information. In this paper …

Phase retrieval from incomplete data via weighted nuclear norm minimization

Z Li, M Yan, T Zeng, G Zhang - Pattern Recognition, 2022 - Elsevier
Recovering an unknown object from the magnitude of its Fourier transform is a phase
retrieval problem. Here, we consider a much difficult case, where those observed intensity …

Generative principal component analysis

Z Liu, J Liu, S Ghosh, J Han, J Scarlett - arXiv preprint arXiv:2203.09693, 2022 - arxiv.org
In this paper, we study the problem of principal component analysis with generative
modeling assumptions, adopting a general model for the observed matrix that encompasses …